Certified XOR-Spectral Normalization for SAT: Entailed Parity Detection, Elimination, and DRAT-Compatible Progress

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Auteur principal: Paradise, Christopher
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Publié: Zenodo 2026
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_version_ 1866901998207500288
author Paradise, Christopher
author_facet Paradise, Christopher
contents <p class="p1">This paper presents a sound algebraic theory module for SAT based on entailed XOR normalization. It defines verifier-checkable XOR-witness certificates, an XOR store represented as a linear system over <span class="s1">\mathbb{F}_2</span>, Gaussian elimination for inconsistency and consequence derivation, and an XOR-LEARN step that can compile newly derived parity consequences back into CNF with checker-accepted implication proofs. The module is intentionally bounded: it does not assume that all hard SAT structure is linear, but when entailed parity is present it provides a certified progress move compatible with DRAT/FRAT-style proof checking. Its contribution is methodological: a concrete algebraic auxiliary layer sitting between clause-based proof systems and linear structure, with explicit soundness guarantees and clean integration into a verifier-driven SAT router.</p>
format Recurso digital
id zenodo_https___doi_org_10_5281_zenodo_19508205
institution Zenodo
language
publishDate 2026
publisher Zenodo
record_format zenodo
spellingShingle Certified XOR-Spectral Normalization for SAT: Entailed Parity Detection, Elimination, and DRAT-Compatible Progress
Paradise, Christopher
certified XOR normalization, SAT proof systems, entailed parity detection, XOR elimination, DRAT-compatible learning, FRAT-compatible implications, algebraic SAT methods, Gaussian elimination over F2, certificate-driven SAT, auxiliary theory modules
<p class="p1">This paper presents a sound algebraic theory module for SAT based on entailed XOR normalization. It defines verifier-checkable XOR-witness certificates, an XOR store represented as a linear system over <span class="s1">\mathbb{F}_2</span>, Gaussian elimination for inconsistency and consequence derivation, and an XOR-LEARN step that can compile newly derived parity consequences back into CNF with checker-accepted implication proofs. The module is intentionally bounded: it does not assume that all hard SAT structure is linear, but when entailed parity is present it provides a certified progress move compatible with DRAT/FRAT-style proof checking. Its contribution is methodological: a concrete algebraic auxiliary layer sitting between clause-based proof systems and linear structure, with explicit soundness guarantees and clean integration into a verifier-driven SAT router.</p>
title Certified XOR-Spectral Normalization for SAT: Entailed Parity Detection, Elimination, and DRAT-Compatible Progress
topic certified XOR normalization, SAT proof systems, entailed parity detection, XOR elimination, DRAT-compatible learning, FRAT-compatible implications, algebraic SAT methods, Gaussian elimination over F2, certificate-driven SAT, auxiliary theory modules
url https://doi.org/10.5281/zenodo.19508205